An online music club has a one-time registration fee of $20 and charges $0.50 for each song download. If Ella has $50.00 to join the club and buy songs, which inequality gives the maximum number of songs, s, she can buy?(1 point)
Responses
s≥30
s is greater than or equal to 30
s≤30
s is less than or equal to 30
s≥60
s is greater than or equal to 60
s≤60
To determine the maximum number of songs Ella can buy, we need to consider the cost of the registration fee and the cost of the song downloads.
Given that Ella has $50.00, the inequality should represent the maximum number of songs she can buy within that budget.
The registration fee is a one-time cost of $20.
The song downloads cost $0.50 each.
Therefore, Ella's budget for song downloads is $50.00 - $20.00 = $30.00.
To determine the maximum number of songs, s, she can buy, we divide her budget for song downloads by the cost per song download:
s ≤ 30.
Therefore, the correct inequality that gives the maximum number of songs Ella can buy is s ≤ 30.
Mark and Anson each have a video game collection.
The number of video games in Mark collection can be represented by x.
The number of video games in Anson collection is 5 times the number in Mark collection.
The total number of video games is no more than 72.
What is the solution set for x, the number of video games in Mark’s collection?
(1 point)
Responses
x≤12
x is less than or equal to 12
x≤−12
x is less than or equal to negative 12
x≥15
x is greater than or equal to 15
x≥−1
Let's represent the number of video games in Mark's collection by x.
According to the given information, the number of video games in Anson's collection is 5 times the number in Mark's collection, so this can be represented as 5x.
The total number of video games is no more than 72, which means the sum of the number of video games in Mark's and Anson's collections is less than or equal to 72:
x + 5x ≤ 72
6x ≤ 72
To solve for x, we divide both sides of the inequality by 6:
x ≤ 72/6
x ≤ 12
Therefore, the solution set for x, the number of video games in Mark's collection, is x ≤ 12.
What is the solution set for 12−6x>24
?(1 point)
Responses
x>2
x is greater than 2
x<2
x<2
x>−2
x is greater than negative 2
x<−2
To solve the inequality 12 - 6x > 24, we can first subtract 12 from both sides:
-6x > 12
Next, we divide both sides by -6. When dividing by a negative number, we need to reverse the direction of the inequality:
x < -2
Therefore, the correct solution set for the inequality 12 - 6x > 24 is x < -2.